An Introduction to Applied Probability

Pierre Brémaud (Autor)

Buch | Hardcover

XIII, 492 Seiten

2024 | 2024
Springer International Publishing (Verlag)
978-3-031-49305-8 (ISBN)

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This book provides the elements of probability and stochastic processes of direct interest to the applied sciences where probabilistic models play an important role, most notably in the information and communications sciences, computer sciences, operations research, and electrical engineering, but also in fields like epidemiology, biology, ecology, physics, and the earth sciences.
The theoretical tools are presented gradually, not deterring the readers with a wall of technicalities before they have the opportunity to understand their relevance in simple situations. In particular, the use of the so-called modern integration theory (the Lebesgue integral) is postponed until the fifth chapter, where it is reviewed in sufficient detail for a rigorous treatment of the topics of interest in the various domains of application listed above.
The treatment, while mathematical, maintains a balance between depth and accessibility that is suitable for theefficient manipulation, based on solid theoretical foundations, of the four most important and ubiquitous categories of probabilistic models:

Markov chains, which are omnipresent and versatile models in applied probability
Poisson processes (on the line and in space), occurring in a range of applications from ecology to queuing and mobile communications networks
Brownian motion, which models fluctuations in the stock market and the "white noise" of physics
Wide-sense stationary processes, of special importance in signal analysis and design, as well as in the earth sciences.

This book can be used as a text in various ways and at different levels of study. Essentially, it provides the material for a two-semester graduate course on probability and stochastic processes in a department of applied mathematics or for students in departments where stochastic models play an essential role. The progressive introduction of concepts and tools, along with the inclusion of numerous examples, also makes this book well-adapted for self-study.

lt;b>Pierre Brémaud graduated from the École Polytechnique and obtained his Doctorate in Mathematics from the University of Paris VI and his PhD from the department of Electrical Engineering and Computer Science at the University of California, Berkeley. He is a major contributor to the theory of stochastic processes and their applications, and has authored or co-authored several reference books and textbooks.

Preface.- Basic Notions.- Discrete Random Variables.- Continuous Random Vectors.- The Lebesgue Integral.- From Integral to Expectation.- Convergence Almost Sure.- Convergence in Distribution.- Martingales.- Markov Chains.- Poisson Processes.- Brownian Motion.- Wide-sense Stationary Processes.- A Review of Hilbert Spaces.- Bibliography.- Index.

Erscheinungsdatum	10.05.2024
Reihe/Serie	Texts in Applied Mathematics
Zusatzinfo	XIII, 492 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Brownian motion • conditional expectation • Continuous-time stochastic processes • Convergence of random variables • Discrete Random Variables • markov chains • Markov Fields • Martingales • Poisson Processes • probability textbook • random vectors • simulation algorithm • stochastic integral • Wide-sense stationary processes • Wiener process
ISBN-10	3-031-49305-2 / 3031493052
ISBN-13	978-3-031-49305-8 / 9783031493058
Zustand	Neuware